Fluid flow meters, such as those disclosed by Dov Ingman in U.S. Pat. Nos. 4,920,794 and 5,069,067 both of which are incorporated herein by reference, measure flow rate of a fluid by measuring undulation of a flexible membrane in response to passage of the fluid through a flow chamber. The flexible membrane spans between two points along the flow path of the fluid and has a length which is long enough to undulate and divide, with a pair of opposing walls, the flowing fluid into discrete quanta, each with a determinable volume. By detecting the motion of the membrane, the movement of the fluid quanta and therefore the flow rate of the fluid can be measured.
Among the factors affecting the performance of the above described flexible membrane fluid flow meters are the physical properties of the membrane.
For example, an ideal membrane would be one that is formed from material with very low mass and a high modulus of elasticity. Theoretically, with a zero mass membrane, the resonant frequency of the membrane would be infinite and would therefore not resonate or flutter because the actual frequency of motion induced in the membrane by the fluid flow can never reach infinity. In addition, an ideal membrane should require only negligible energy to move in response to the fluid flow so that it can measure very low or near zero flow rates.
The mass of a membrane is proportional to its thickness. However, the stiffness of a membrane is proportional to the cube of its thickness. Therefore, decreasing the thickness of the membrane to reduce its mass would decrease the stiffness at a greater rate. If the membrane is too thin and the stiffness is reduced too far, a portion of the membrane will lie limply on a membrane face under gravitational force. As a result, a limit to the possible reduction in membrane thickness is the point where the stiffness is reduced to below the level required to maintain membrane shape against the force of gravity.
Moreover, although it is desirable to have the thinnest membrane capable of maintaining its shape against gravity, membrane thickness is generally desirable in order to minimize leakage through the gaps between the edges of the membrane and the side walls of the flow chamber. If the membrane can be made thicker, the required manufacturing tolerances to maintain the effective seal between the membrane edges and the side walls can be relaxed, thereby reducing manufacturing costs.
Thus, the ideal membrane would be relatively thick to minimize sealing problems, of low density to minimize mass and stiff enough to enable it to support its own weight. In other words, the membrane thickness is a trade off between the membrane mass, the required stiffness for supporting its own weight and the required tolerances for maintaining an effective seal against leakage.
Another factor affecting the performance of a flexible membrane fluid flow meter is its durability. One factor affecting the durability of a membrane is the short operating life which could result from membrane fatigue due to repetitive flexing thereof at the clamping points.